Method and apparatus for performing hierarchical super-resolution of an input image

ABSTRACT

Super-resolution refers to a process of recovering the missing high-frequency details of a given low-resolution image. Known single image SR algorithms are often computationally intractable or unusable for most of the practical applications. The invention relates to a method for performing hierarchical super-resolution based on self content neighboring patches information is based on pyramidal decomposition. The intrinsic geometric property of an input LR patch neighborhood is obtained from the input LR patch and its K nearest neighbors taken from different down-scaled versions of the LR image.

FIELD OF THE INVENTION

The invention relates to a method for performing hierarchical super-resolution of an input image, and to an apparatus for performing hierarchical super-resolution of an input image. The invention relates also to a method for averaging of pixels in performing super-resolution by using block-based predictions, and to an apparatus for averaging of pixels in performing super-resolution by using block-based predictions.

BACKGROUND

Super-resolution (SR) refers to a process of recovering the missing high-frequency details of a given low-resolution (LR) image. In other words, SR produces a high-resolution (HR) image with clear and detailed contents using one or more LR observations. One class of SR processes relates to Single Image Super-Resolution.

Various image up-sampling techniques are known, including some that use a single low-resolution image and some that are not using any external information or database. Some SR techniques use upsampling of spatial texture patches for giving local geometric similarities of LR and HR image patch spaces.

The following is an outline of how this problem is currently addressed. Classical SR methods, e.g. [1]-[3], try to fuse a set of LR images in order to recover the unknown HR image. These algorithms assume that the missing high-frequency information is distributed implicitly along the LR observations, and the HR image can be recovered successfully if there is enough number of LR images. The quality of the reconstructed HR image therefore depends highly on the amount of data available in the LR images.

However, in practice, insufficient number of LR observations, registration (i.e. motion estimation) errors, and unknown point spread function (PSF) limit the applicability of these multi-image SR methods to small upscaling ratios, which is less than 2 under general conditions [4].

Example-based methods have been proposed in order to overcome the limitations of classical multi-image SR. In [5], LR and HR image patch pairs are collected from other natural images, and low- and high-frequency relations of these patches are learned via a Markov network using belief propagation. This method has later been simplified in [6] to give a fast and approximate solution to the Markov network, with a sequence of predictions of HR patches by a nearest neighbor (NN) search from the database of the collected training examples. The missing high-frequency details are estimated (“hallucinated”) according to the local LR image information and the high-frequency patch compatibilities of the recently recovered part of the HR image. Similar NN-based approaches have largely been exploited in the context of example-based texture synthesis [7]-[9], and have been shown to be beneficial in different image processing applications, e.g. in [10]-[12].

Nevertheless, one is required here to construct databases of enormous numbers of training LR and HR patch pairs in order to be representative enough for SR, and thus, this is computationally intractable or unusable for most of the practical applications.

SUMMARY OF THE INVENTION

The invention improves known image up-sampling techniques by using a super-resolution (SR) method from a single low-resolution image, without using any external information or database. At least one embodiment of the invention concerns principally the use of spatial texture patches giving local geometric similarities of low-resolution (LR) and high-resolution (HR) image patch spaces.

At least one embodiment of the present invention improves the image up-sampling technique by using a pyramidal super-resolution method from a single LR image, without using any external information or database. In one embodiment, the mean of each block is calculated and subtracted before processing the block, and added again later. It is noted that the terms block and patch are used synonymously herein, as usual in the art.

In general, the invention concerns intrinsic single image SR, and relies on local geometric similarities of LR and HR image patch spaces. The intrinsic geometric property of an input (mean subtracted or not, see below) LR patch neighborhood is obtained from the input LR patch and its K nearest neighbors (K-NN) taken from across scales of the LR image (i.e. from different scales).

According to one embodiment of the invention, a method for performing hierarchical SR of an input image comprises steps of dividing the input image into patches, performing spatial decomposition of the input image to at least two lower decomposition levels, wherein at least two lower decomposition level images are obtained, and generating an empty upsampled frame, wherein for each patch of the input image a corresponding upsampled patch in the upsampled frame is generated. Then, for each current patch of the input image, the method comprises performing the steps of searching in the lower decomposition level images one or more similar patches of same size as the current patch, for each of the similar patches found in the searching step determining its respective parent patch in the next higher decomposition level, weighting the determined parent patches, accumulating the weighted determined parent patches to is obtain an upsampled high-resolution patch, and replacing in the up-sampled frame an upsampled patch corresponding to the current patch with the upsampled high-resolution patch.

In one embodiment, the invention concerns a corresponding apparatus, as disclosed in claim 12 and described below.

In one embodiment, the local LR geometry is characterized linearly with the locally linear embedding (LLE) [13] reconstruction coefficients of the input LR patch from its K-NN. The HR embedding is then estimated (“hallucinated”) from the corresponding (mean subtracted or not, see below) HR parents of the found K-NN of the input LR patch, by assuming that the local LR geometry has been preserved in the HR patch space. An estimate of the current HR patch is then obtained by adding the mean value of the input LR patch.

In one embodiment, the invention relates to a method for averaging of pixels in performing super-resolution by using block-based predictions, wherein LLE is used and wherein the pixels are from source blocks that are overlapping. The method comprises steps of determining sparsity factors of the source blocks, and combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.

In one embodiment, the invention relates to an apparatus for averaging of pixels in performing super-resolution by using block-based predictions, wherein LLE is used and wherein the pixels are from source blocks that are overlapping. The apparatus comprises a first processing unit for determining sparsity factors of the source blocks, and a second processing unit for combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels. The first and second processing units may be implemented as a single processing unit.

Further objects, features and advantages of the invention will become apparent from a consideration of the following description and the appended claims when taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention are described with reference to the accompanying drawings, which show in

FIG. 1 the structure of upsampling a single-image for achieving super-resolution through across-scale neighbor embedding;

FIG. 2 an exemplary relationship between the number of non-zero coefficients in a block and a normalized weighting factor that is to be used for the block;

FIG. 3 a flow-chart of a method for performing hierarchical super-resolution of an input image, according to one embodiment of the invention;

FIG. 4 a detail flow-chart of the step of searching similar patches in the lower decomposition level images;

FIG. 5 a detail flow-chart of the step of replacing an upsampled patch in the up-sampled frame;

FIG. 6 a flow-chart of a method for averaging of pixels in performing super-resolution, according to one embodiment of the invention;

FIG. 7 the structure of an apparatus for performing hierarchical super-resolution of an input image;

FIG. 8 the structure of an apparatus for averaging of pixels in performing super-resolution; and

FIG. 9 a high-level flow-chart of a method according to one embodiment of the invention.

DETAILED DESCRIPTION

FIG. 1 shows Single-image super-resolution through across-scale neighbor embedding, as explained in the following. For performing a super resolution of a low resolution input I₀ image, the algorithm can be resumed as following.

A high-level flow-chart of the algorithm, as shown in FIG. 9, comprises at least a step A1 of L+1 levels Pyramid construction, a step A2 of LR patch estimation and respective HR patch reconstruction, and a step A3 of overlapping of the LR/HR patch estimations.

First, the L+1 levels Pyramid construction process A1 is described. It comprises the following steps, which are explained with reference to FIG. 1.

The input I₀ (LR, pyramid level I=0) image is filtered and downsampled, of a given ratio r_(d), by a low pass filter, wherein the low frequency image I⁻¹ is obtained. The previously downsampled image I⁻¹ is filtered and down sampled again by a low pass filter, wherein the low frequency image I⁻² is obtained, etc. By repetition of this process, more spatial decomposition levels can be obtained. Finally, a down sampled image I_(−L+2) is filtered and downsampled by a low pass filter, wherein the last low frequency image I_(−L+1) is obtained. An empty HR image I₁ is created, wherein ratio of the sizes of I₁ and I₀ is of the inverse ratio than I₀ to I⁻¹, that is: I₁/I₀=I₀/I⁻¹, or: the upsampling factor r_(u) is the inverse of the downsampling factor r_(d).

Finally, the pyramid is composed of Level 1 (bottom of the upside-down pyramid shown in FIG. 1) being the HR image resolution (which is to be reconstructed), Level 0 being the input LR image, and Level −L+2 being the lowest resolution image (top of the upside-down pyramid in FIG. 1).

Second, the step A2 of LR patch estimation and HR patch reconstruction from lowest frequency patches is described. Two alternative embodiments are disclosed: one is called “Luminance based”, and the other is called “Gradient based”.

The Luminance based solution comprises LR patch estimation, HR patch reconstruction and HR image reconstruction as follows.

LR patch estimation comprises steps of determining in the input image I₀ a first patch P_(n) at a first position, wherein n is the index of the current path in I₀, searching the K nearest neighbors (K-NN) taken from lower scales I⁻¹, I⁻², . . . , I_(−L+1) of the LR image I₀, and characterizing linearly with a locally linear embedding (e.g. Locally Linear Embedding, LLE from [13]) reconstruction coefficients of the input LR patch P_(n) from its K-NN PN_(n,k) with the respective weighting factor w_(n,k). The K-NN being the K best matching patches PN_(n,k) (with the previous first patch P₀) according to a given criterion (e.g. SAD, SSE). SAD (sum-of-absolute-differences) and SSE (sum-of-squared-errors) are commonly known criteria in the technical field concerned.

HR patch reconstruction comprises building (also referred to as synthesizing) the HR patch P_(Hn) embedding from the corresponding HR parents PPN_(n,k) of the found K-NN of the input LR patch PN_(n,k) with the respective previous weighting factor w_(n,k), in which precisely the current HR P_(Hn) patch of the I₁ image is the homologous of the P_(n) patch of the input image I₀, and the HR parents PPN_(n,k) issuing from I₀, I⁻¹, . . . , I_(−L+2) images of the pyramid are the homologous of the PN_(n,k) patches issuing from the I⁻¹, I⁻², . . . , I_(−L+1) images of the pyramid.

HR image reconstruction comprises repeating the LR patch estimation and HR patch reconstruction for all the patches/couples of the patches of the LR/HR image.

The Gradient based solution (i.e. mean subtracted of luminance) comprises LR patch estimation, HR patch reconstruction and HR image reconstruction as follows.

LR patch estimation comprises determining in the input image I₀ a first patch P_(n) at a first position, wherein n is the index of the current path in I₀ and the mean of the block is subtracted, searching the K nearest neighbors K-NN taken from lower scales I⁻¹, I⁻², . . . , I_(−L+1) of the LR image I₀, and characterizing linearly with a locally linear embedding (e.g. LLE) reconstruction coefficients of the input LR patch P_(n) from its K-NN PN_(n,k) with the respective weighting factor w_(n,k). The K-NN are the K best matching patches PN_(n,k) (with the previous first patch P₀) according to a given criterion (e.g. SAD, SSE), wherein at each block PN_(n,k) the mean (i.e. its own individual mean) is also subtracted.

HR patch reconstruction comprises building (also referred to as synthesizing) the HR patch P_(Hn) embedding from the corresponding (with the mean, i.e. its own mean, subtracted) HR parents PPN_(n,k) of the found K-NN of the input LR patch PN_(n,k) with the respective previous weighting factor w_(n,k), in which precisely: the current HR P_(Hn) patch of the I₁ image is the homologous of the P_(n) patch of the input image I₀, and the HR parents PPN_(n,k) issuing from I₀, I⁻¹, . . . , I_(−L+2) images of the pyramid are the homologous of the PN_(n,k) patches issuing from the I⁻¹, I⁻², . . . , I_(−L+1) images of the pyramid. Finally, the mean value of the input LR (input I₀ image) patch is added to the current reconstructed HR patch.

HR image reconstruction comprises repeating the LR patch estimation and HR patch reconstruction for all the patches/couples of the LR/HR images.

The next step A3, after L+1 levels pyramid reconstruction A1 and LR patch estimation and HR patch reconstruction A2, is the overlapping of LR/HR patch estimations, i.e. synthesis from lowest frequency patches. It comprises, in one embodiment, at least one of mean averaging and sparsity weighting averaging.

Mean averaging comprises that, after for each patch in the LR image I₀ a HR embedding has been calculated, an overlap between patches is allowed in order to average, for each HR pixel, all the pixel contributions issued from the reconstructed blocks overlapping each current pixel.

Sparsity weighting averaging comprises that the estimated overlap region pixels are then weighted according to a sparsity-based measure, in order to preserve the dominant structures. Then the weighting average is realized according to the sparsity degree of the block in which the overlapped pixel is issued. The sparsity weighting factor can be a function of the number of DCT coefficients of the block, or more complex the number of atoms representing the block in case of sparse representation such as “Matching Pursuit” (MP) or “Orthogonal Matching Pursuit” (OMP).

In one embodiment, an additional final step is iterative back projection (not shown in FIG. 9). This step consists in the application of a known iterative back projection process, which ensures that the recovered HR image produces the same reference LR image as observed. That approach resides in adding recursively (at the iteration k), to the reconstructed HR_(k) image result, the up-sampled (and low pass filtered) difference between the original input LR image I₀ and the down sampled HR_(k−1) image. The operation is repeated for a predefined maximum number of iterations. Usually, e.g. 20 iterations are sufficient. A generally applicable range is 10-30 iterations, however less iterations may be sufficient in some cases.

Various patch sizes are possible. Particularly advantageous patch sizes for low resolution are 3×3, 5×5 and 7×7 pixels (with 5×5 giving the best results at least for 2×2 up-scaling). For HR, the homologous sizes are: 6×6, 10×10 and 14×14 pixels. Also, various other subsampling factors from one image to the next can be used, different from 2. It is possible to extend the method for factors of e.g. 3 or 4. This extension is achieved by adjusting LR and HR patch sizes, and down-scaled versions of the LR image. Further, as another option, up-sampling by a factor of 2 can be applied twice in order to get an up-scaling of factor 4, or up-sampling by a factor of 3 can be applied twice in order to get an up-scaling of factor 6 etc.

For each patch in the LR image, a HR embedding preserving the local geometry of the LR neighborhood is calculated. An overlap between patches is allowed as much as possible in order to enforce the local compatibility and smoothness constraints in the target HR image. Exemplarily, the patches overlap by 1 pixel or 2 pixels per dimension.

The overlap region pixels can be then linearly combined depending on a sparse representations based weighting measure. In this method, a concatenation of input LR patch and estimated HR patch can be decomposed over a dictionary which is composed of LR and HR image patches taken from the LR image and its across scales.

In one embodiment, the patches are weighted depending on the sparseness of their representation, i.e., the sparsest representation is given the highest weight, and so on. In one embodiment, the weight depends on the number of non-zero coefficients (e.g. DCT coefficients) (after thresholding) of the patch. In one embodiment, the weights are then calculated using an exponential function, as shown in FIG. 2, according to:

W=exp(f(number of non-zero coefficient))

FIG. 2 shows an exemplary relationship between the number of non-zero coefficients in a block (actually “non-zero” means above a minimum threshold that is near zero) and a normalized weighting factor that is to be used for the block. As shown, the more non-zero coefficients a block has, the lower is the weighting factor.

If a sparse representation of the patch (e.g. MP, OMP) is used, here in the context of sparse representation an “atom” (issuing of a dictionary which is composed of N atoms) is similar to a “basis function” of DCT, knowing an atom and the basis function are represented in the spatial domain. Here the weight depends also on the number of non-zero coefficients.

Finally, to satisfy the global reconstruction constraint (i.e.: the recovered HR image should produce the same reference LR image as observed), an iterative back projection method [1],[2] is adopted in one embodiment. Then, the final HR image estimate is assumed to be the result from the back-projection algorithm S9.

In one embodiment, the overall algorithm is composed of:

-   -   a pyramidal SR algorithm, e.g. LLE based,     -   plus sparsity averaging (of the reconstructed overlapped blocks)     -   and (optionally)+back projection.

Advantageously, an algorithm according to the invention outperforms the algorithms known in the art.

FIG. 3 shows a flow-chart of a method for performing hierarchical super-resolution of an input image, according to one embodiment of the invention. In this embodiment, a method 10 for performing hierarchical super-resolution of an input image I₀ comprises steps of dividing S1 the input image I₀ into patches P_(n), performing S2 spatial decomposition of the input image I₀ to at least two lower decomposition levels, wherein at least two lower decomposition level images I⁻¹, I⁻² are obtained, and generating S3 an empty upsampled frame I₁, wherein for each patch P_(n) of the input image a corresponding upsampled patch in the upsampled frame I₁ is generated. Then, for each current patch P_(n) of the input image I₀ the following steps are performed.

In the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3) of same size as the current patch, are searched S4. For each of the similar patches PN_(n,1), PN_(n,2), PN_(n,3) found in the searching step, its respective parent patch PPN_(n,1), PPN_(n,2), PPN_(n,3) in the next higher decomposition level I₀, I⁻¹ is determined S5. The determined parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3) are weighted S6 with weighting factors w₁, w₂, w₃, wherein weighted determined parent patches are obtained. The weighted determined parent patches are accumulated S7, wherein an upsampled high-resolution patch P_(Hn) is obtained. Finally, an upsampled patch corresponding to the current patch I₀ is replaced S8 in the up-sampled frame I₁ with the upsampled high-resolution patch P_(Hn).

A first decision step D1 determines whether or not more all potentially similar patches (in the various lower levels) have been investigated, and a second decision step D2 determines whether or not all patches of the input image have been processed.

Note that in the determining step S5 the parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3) found in the next higher decomposition level I₀, I⁻¹ are larger than the respective current patch.

FIG. 4 shows a detail flow-chart of one embodiment of the step of searching similar patches in the lower decomposition level images. In this embodiment, a mean of each current patch is calculated S41 and a mean of each similar patch is calculated S42. The mean of the current patch is subtracted S43 from each pixel value of the current patch.

The mean of each similar patch is subtracted S44 from each pixel value of the respective similar patch. This is performed in the step of searching in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3). Note that step S43 can be performed before or after step S42.

FIG. 5 shows a detail flow-chart of one embodiment of the step of replacing an upsampled patch in the upsampled frame. In this embodiment, the mean of each current patch is added S81 to each pixel value of the upsampled patch corresponding to the current patch, and then the actual insertion S82 of the upsampled patch in the up-sampled frame I₁ is done, whereby the upsampled patch replaces the default patch in the HR image.

FIG. 6 shows a flow-chart of a method for averaging of pixels in performing SR, according to one embodiment of the invention. The method 60 for averaging of pixels in performing super-resolution by using block-based predictions, wherein LLE is used and wherein the pixels are from source blocks that are overlapping, comprises steps of determining S6_1 sparsity factors of the source blocks, and combining S6_2 the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.

FIG. 7 shows the structure of an apparatus for performing hierarchical super-resolution of an input image, wherein the input image I₀ is divided into patches P_(n). The apparatus 70 comprises a spatial decomposition unit SDU, an upsampling unit UPU, and a processing unit PU. Further units, which may be separate units or part of the processing unit, are a search unit P_SU, a parent patch determining unit P_PDU, a weighting unit P_WU, an accumulation unit P_AU and a patch insertion unit P_PIU (or patch replacement unit, see above).

The spatial decomposition unit SDU performs spatial decomposition of the input image I₀ to at least two lower decomposition levels, wherein at least two lower decomposition level images I⁻¹, I⁻² with different spatial resolutions are obtained.

The upsampling unit UPU generates an empty upsampled frame I₁, wherein for each patch P_(n) of the input image a corresponding upsampled patch in the upsampled frame I₁ is generated.

In one embodiment, the processing unit PU performs for each current patch P_(n) of the input image I₀ the steps of searching in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3) of same size as the current patch, for each of the similar patches PN_(n,1), PN_(n,2), PN_(n,3) found in the searching step, determining its respective parent patch PPN_(n,1), PPN_(n,2), PPN_(n,3) in the next higher decomposition level I₀, I⁻¹, wherein the parent patches are larger than the current patch, weighting the determined parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3), wherein weighted determined parent patches are obtained, accumulating the weighted determined parent patches, wherein an upsampled high-resolution patch P_(Hn) is obtained, and replacing in the up-sampled frame I₁ an upsampled patch corresponding to the current patch I₀ with the upsampled high-resolution patch P_(Hn).

In other embodiments, one or more of the following separate units are used.

In one embodiment, the searching in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3) of same size as the current patch is done by a search unit P_SU.

In one embodiment, the determining, for each of the similar patches PN_(n,1), PN_(n,2), PN_(n,3) found in the searching step, a respective parent patch PPN_(n,1), PPN_(n,2), PPN_(n,3) in the next higher decomposition level is done by a parent patch determining unit P_PDU. Note that generally the parent patches are larger than the current patch (see FIG. 1).

In one embodiment, the weighting the determined parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3) in order to obtain weighted determined parent patches is done by a weighting unit P_WU. In one embodiment, the accumulating the weighted determined parent patches in order to obtain an upsampled high-resolution patch P_(Hn) is done by an accumulation unit P_AU. In one embodiment, the replacing an upsampled patch corresponding to the current patch I₀ with the upsampled high-resolution patch P_(Hn) in the up-sampled frame I₁ is done by an insertion unit P_PIU.

FIG. 8 shows the structure of an apparatus for averaging of pixels in performing super-resolution, wherein Local Linear Embedding (LLE) is used and wherein the pixels are from source blocks that are overlapping. The apparatus 80 comprises

a first processing unit, e.g. a sparsity determining processing unit SFPU, for determining sparsity factors of the source blocks, and

a second processing unit, e.g. a pixel combining processing unit PCPU, for combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.

In general, the present invention relates to at least one of

a hierarchical SR algorithm based on self content neighboring patches information that is based on pyramidal decomposition, with or without subtracting the mean of the block, and optimal pixel averaging of block-based predictions using a sparsity factor instead of the classical averaging in the context of LLE SR techniques.

An advantage of the invention is that the invention improves the performance of rendering up-sampled images. Up-sampled images can be rendered quicker and with reduced computation.

Possible advantageous applications of the invention comprise video distribution and display technologies, and applications related to video compression (e.g. spatial scalability) and content representation.

The disclosed method can be implemented in an apparatus for performing the method, which has separate units, each for performing one of the steps. Further, the method can be computer-implemented for execution on a processor.

In one embodiment of the invention, a computer-readable storage medium comprises program data that, when executed on a processor, cause the processor to perform a method for performing hierarchical super-resolution of an input image, as disclosed above with reference to FIGS. 1 and 3.

In one embodiment of the invention, a computer-readable storage medium comprises program data that, when executed on a processor, cause the processor to perform a method for averaging pixels in performing super-resolution by using block-based predictions, as disclosed above with reference to FIG. 6.

In one embodiment, the invention concerns a method for performing hierarchical super-resolution based on self content neighboring patches information, comprising a step of pyramidal decomposition. In one embodiment, the mean of a block is subtracted. In another embodiment, the mean of a block is not subtracted. In one embodiment, the pyramidal super-resolution algorithm includes an algorithm giving a weighted combination, wherein weights for said weighted combination are determined by solving a constrained least square problem, such as a neighbors embedding algorithm. In one embodiment, the pyramidal super-resolution algorithm is a neighbors embedding algorithm such as LLE or non-negative matrix factorization (NMF).

In one embodiment, the invention concerns a method for optimal pixel averaging of block-based predictions, especially in the context of LLE super-resolution, using a sparsity factor (instead of classical averaging). In one embodiment, the sparsity factor is used as a weighting factor.

In one embodiment of the invention, a method 10 for performing hierarchical super-resolution of an input image I₀, comprises steps of

dividing S1 the input image I₀ into patches P_(n),

performing S2 spatial decomposition of the input image to at least two lower decomposition levels, wherein at least two lower decomposition level images are obtained,

generating S3 an empty upsampled frame I₁, wherein for each patch P_(n) of the input image a corresponding upsampled patch in the upsampled frame I₁ is generated, and performing, for each current patch P_(n) of the input image I₀, the steps of

searching S4 in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3) of same size as the current patch,

determining S5, for each of the similar patches PN_(n,1), PN_(n,2), PN_(n,3) found in the searching step, its respective parent patch PPN_(n,1), PPN_(n,2), PPN_(n,3) in the next higher decomposition level I₀, I⁻¹, wherein the parent patches are larger than the current patch,

weighting S6 the determined parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3) using individual weights w₁, w₂, w₃, wherein weighted determined parent patches are obtained,

accumulating S7 the weighted determined parent patches, wherein an upsampled high-resolution patch P_(Hn) is obtained, and

replacing S8, in the up-sampled frame I₁, an upsampled patch corresponding to the current patch I₀ with the upsampled high-resolution patch P_(Hn).

In one embodiment, the method comprises in the step of searching similar patches in the lower decomposition level images, calculating a mean of each current patch and a mean of each similar patch S41, S42 and subtracting S43, S44 the mean from each pixel value of the respective patch. Further, in the step of replacing, the mean of each current patch is added S81 to each pixel value of the upsampled patch corresponding to the current patch.

In one embodiment, the method comprises, in the step of searching in the lower decomposition level images one or more similar patches, determining a similarity according to a luminance value of the pixels in the patches.

In one embodiment, the method comprises, in the step of searching in the lower decomposition level images one or more similar patches, determining a similarity according to a luminance gradient of the patches.

In one embodiment, the method comprises determining weights used for said weighting from a sparsity of the patch, wherein the sparsity corresponds to a number of non-zero DCT coefficients in the patch.

In one embodiment, the method comprises that the patches the input image are partially overlapping, and therefore also the corresponding upsampled patches in the upsampled image are partially overlapping.

In one embodiment, the method comprises, in the steps of weighting and accumulating, calculating a weighted combination, wherein weights for said weighted combination are determined by solving a constrained least square problem. One example mentioned above is the well-known least square algorithm.

In one embodiment, the method comprises, in the pyramidal super-resolution algorithm, a neighbors embedding algorithm. Examples are locally linear embedding (LLE) or non-negative matrix factorization (NMF).

In one embodiment, the method comprises an additional final step of performing iterative back projection (IBP).

In one embodiment, the method comprises determining the parent patch in the next higher decomposition level according to its relative coordinates. That is, the relative coordinates of a patch in the lower level and those of its parent patch in the higher decomposition level are the same (such as e.g. at 10% of the height and 40% of the width). This may in principle comprise determining the relative coordinates of a patch in the lower level, determining a position having the same relative coordinates in the higher decomposition level, and placing the parent patch at the determined position in the higher decomposition level.

In one embodiment, the invention relates to a method 60 for averaging of pixels in performing super-resolution by using block-based predictions, wherein Local Linear Embedding is used and wherein the pixels are from source blocks that are overlapping. The method comprises steps of determining S6_1 sparsity factors of the source blocks, and combining S6_2 the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.

In one embodiment, the invention relates to an apparatus 70 for performing hierarchical super-resolution of an input image I₀, wherein the input image I₀ is divided into patches P_(n). The apparatus comprises

a spatial decomposition unit SDU for performing spatial decomposition of the input image I₀ to at least two lower decomposition levels, wherein at least two lower decomposition level images (I⁻¹, I⁻²) are obtained,

an upsampling unit UPU for generating an empty upsampled frame I₁, wherein for each patch P_(n) of the input image a corresponding upsampled patch in the upsampled frame I₁ is generated, and

a processing unit PU for performing for each current patch P_(n) of the input image I₀ the steps of

searching in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3) of same size as the current patch,

determining, for each of the similar patches PN_(n,1), PN_(n,2), PN_(n,3) found during the searching, its respective parent patch PPN_(n,1), PPN_(n,2), PPN_(n,3) in the next higher decomposition level I₀, I⁻¹, wherein the parent patches are larger than the current patch,

weighting the determined parent patches PPN_(n,1), PPN_(n,2), PPN_(n,3), wherein weighted determined parent patches are obtained,

accumulating the weighted determined parent patches, wherein an upsampled high-resolution patch P_(Hn) is obtained, and

replacing or inserting, in the up-sampled frame I₁, an upsampled patch corresponding to the current patch I₀ with the upsampled high-resolution patch P_(Hn). Generally, the apparatus may also comprise an image dividing unit for dividing the input image I₀ into patches P_(n), so that also images that are not already divided may be processed.

As described above, the apparatus may comprise one or more separate units of a search unit P_SU, a parent patch determining unit P_PDU, a weighting unit P_WU, an accumulation unit P_AU and a patch insertion unit P_PIU.

In one embodiment of the apparatus, in the unit for searching in the lower decomposition level images I⁻¹, I⁻² one or more similar patches PN_(n,1), PN_(n,2), PN_(n,3), a mean of each current patch and a mean of each similar patch is calculated and subtracted from each pixel value of the respective patch, and in the unit P_PIU for patch insertion or patch replacement, the mean of each current patch is added to each pixel value of the upsampled patch corresponding to the current patch.

In one embodiment, the apparatus further comprises an additional iterative back projection unit.

In one embodiment, the invention relates to an apparatus 80 for averaging of pixels in performing super-resolution by using block-based predictions, wherein Local Linear Embedding is used and wherein the pixels are from source blocks that are overlapping. The apparatus comprises a first processing unit SFPU for determining sparsity factors of the source blocks, and a second processing unit PCPU for combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.

While there has been shown, described, and pointed out fundamental novel features of the present invention as applied to preferred embodiments thereof, it will be understood that various omissions and substitutions and changes in the apparatus and method described, in the form and details of the devices disclosed, and in their operation, may be made by those skilled in the art without departing from the spirit of the present invention. It is expressly intended that all combinations of those elements that perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Substitutions of elements from one described embodiment to another are also fully intended and contemplated.

It will be understood that the present invention has been described purely by way of example, and modifications of detail can be made without departing from the scope of the invention.

Each feature disclosed in the description and (where appropriate) the claims and drawings may be provided independently or in any appropriate combination. Features may, where appropriate be implemented in hardware, software, or a combination of the two. Connections may, where applicable, be implemented as wireless connections or wired, not necessarily direct or dedicated, connections.

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[6] Freeman, W. T., Jones, T. R., Pasztor, E. C.: Example-based super-resolution. IEEE Comp. Graph. Appl. 22 (2002)

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1-15. (canceled)
 16. A method for performing hierarchical super-resolution of an input image, comprising steps of dividing the input image into patches; performing spatial decomposition of the input image to at least two lower decomposition levels, wherein at least two lower decomposition level images are obtained; generating an empty upsampled frame, wherein for each patch of the input image a corresponding upsampled patch in the upsampled frame is generated; and for each current patch of the input image, performing the steps of searching in the lower decomposition level images one or more similar patches of same size as the current patch; for each of the similar patches found in the searching step, determining its respective parent patch in the next higher decomposition level, wherein the parent patches are larger than the current patch; weighting the determined parent patches, wherein a weight used for weighting a patch is determined from a sparsity of the patch, wherein the sparsity corresponds to a number of non-zero DCT coefficients in the patch, and wherein weighted determined parent patches are obtained; accumulating the weighted determined parent patches, wherein an upsampled high-resolution patch is obtained; and replacing, in the up-sampled frame, an upsampled patch corresponding to the current patch with the upsampled high-resolution patch.
 17. Method according to claim 16, wherein, in the step of searching in the lower decomposition level images one or more similar patches, a mean of each current patch and a mean of each similar patch is calculated and subtracted from each pixel value of the respective patch, and wherein in the step of replacing, the mean of each current patch is added to each pixel value of the upsampled patch corresponding to the current patch.
 18. Method according to claim 16, wherein, in the step of searching in the lower decomposition level images one or more similar patches, a similarity is determined according to a luminance of the pixels in the patches.
 19. Method according to claim 16, wherein, in the step of searching in the lower decomposition level images one or more similar patches, a similarity is determined according to a luminance gradient of the patches.
 20. Method according to claim 16, wherein the patches the input image are partially overlapping and the corresponding upsampled patches in the upsampled image are partially overlapping.
 21. Method according to claim 16, wherein the steps of weighting and accumulating comprise calculating a weighted combination, wherein weights for said weighted combination are determined by solving a constrained least square problem.
 22. Method according to claim 16, wherein the pyramidal super-resolution algorithm is a neighbors embedding algorithm.
 23. Method according to claim 16, further comprising an additional step of performing back-projection.
 24. Method according to claim 16, wherein the parent patch in the next higher decomposition level is determined according to its relative coordinates.
 25. A method for averaging of pixels in performing super-resolution by using block-based predictions, wherein Local Linear Embedding is used and wherein the pixels are from source blocks that are overlapping, the method comprising steps of determining sparsity factors of the source blocks; combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.
 26. An apparatus for performing hierarchical super-resolution of an input image, wherein the input image is divided into patches, the apparatus comprising spatial decomposition unit for performing spatial decomposition of the input image to at least two lower decomposition levels, wherein at least two lower decomposition level images are obtained; upsampling unit for generating an empty upsampled frame, wherein for each patch of the input image a corresponding upsampled patch in the upsampled frame is generated; and processing unit for performing for each current patch of the input image the steps of in a search unit, searching in the lower decomposition level images one or more similar patches of same size as the current patch; for each of the similar patches found in the searching step, determining in a parent patch determining unit its respective parent patch in the next higher decomposition level, wherein the parent patches are larger than the current patch; in a weighting unit, weighting the determined parent patches, wherein a weight used for weighting a patch is determined from a sparsity of the patch, wherein the sparsity corresponds to a number of non-zero DCT coefficients in the patch, and wherein weighted determined parent patches are obtained; in an accumulation unit, accumulating the weighted determined parent patches, wherein an upsampled high-resolution patch is obtained; and replacing in an insertion unit, in the up-sampled frame, an upsampled patch corresponding to the current patch with the upsampled high-resolution patch.
 27. The apparatus according to claim 26, wherein, in the search unit for searching in the lower decomposition level images one or more similar patches, a mean of each current patch and a mean of each similar patch is calculated and subtracted from each pixel value of the respective patch, and wherein in the insertion unit the mean of each current patch is added to each pixel value of the upsampled patch corresponding to the current patch.
 28. An apparatus for averaging of pixels in performing super-resolution by using block-based predictions, wherein Local Linear Embedding is used and wherein the pixels are from source blocks that are overlapping, the apparatus comprising a first processing unit for determining sparsity factors of the source blocks; and a second processing unit for combining the pixels from the source blocks according to weighting factors, wherein the sparsity factor of each source block is used as a weighting factor for its pixels.
 29. Computer-readable storage medium comprising program data that when executed on a processor cause the processor to perform a method according to claim
 16. 30. Computer-readable storage medium comprising program data that when executed on a processor cause the processor to perform a method according to claim
 11. 